Hi Zeb - and welcome to the BBB.
My "spare" PC resembles yours:
Using yahoo messenger v7.5.0.333
Windows XP SP2 (but without any subsequent Windows Updates)
Intel Celeron 800 Mhz, 256 MB RAM
standard XP firewall - no other firewall or antivirus program running.
I have no trouble with pc-to-pc Calls on it - in fact I've just checked, using Task Manager, Performance:
During a CALL my CPU usage seemed to have a constant zigzag pattern ranging from about 20% to 70%, and no sign of any YM crashing/freezing.
As for the YM version, I used to have 7.0 on it, and no major problems there either - so - I figure your PC SHOULD be quite capable...... so maybe there's some OTHER fly in the ointment !?
I'd agree with PK's first 2 suggestions, then as well I suggest being sure that nothing ELSE (unnecessary) is running at the same time as your YM.
Good luck, and keep us posted on progress.
YM is too good to have not working properly (though hey, you're only one of hundreds who DO have problems lately

)
P.S. My PC can also handle Yahoo Games (e.g. Pool, Spades, etc) ok, so there's another difference!?

THAT makes me wonder if perhaps you don't have the right JAVA installed, though I don't THINK a YM Call has any need for anything related to Java.
There's also a Macromedia Flash player that I think YM uses at some time - PERHAPS that could be another avenue to explore later.